The modality of a Borel subgroup in a simple algebraic group of type $E_8$

Let $G$ be a simple algebraic group over an algebraically closed field $k$, where $mathrm{char}, k$ is either 0 or a good prime for $G$. We consider the modality $mathrm{mod}(B : mathfrak u)$ of the action of a Borel subgroup $B$ of $G$ on the Lie algebra $mathfrak u$ of the unipotent radical of $B$, and report on computer calculations used to show that $mathrm{mod}(B:mathfrak u) = 20$, when $G$ is of type $mathrm E_8$. This completes the determination of the values for $mathrm{mod}(B:mathfrak u)$ for $G$ of exceptional type.